Arctangent Series on Pell and Pell-Lucas Polynomials via Cassini-Like Formulae

Q4 Mathematics

Utilitas Mathematica Pub Date : 2024-01-08 DOI:10.61091/um118-01

Dongwei Guo, Wenchang Chu

引用次数: 0

Abstract

By combining the telescoping method with Cassini–like formulae, we evaluate, in closed forms, four classes of sums about products of two arctangent functions with their argument involving Pell and Pell–Lucas polynomials. Several infinite series identities for Fibonacci and Lucas numbers are deduced as consequences.

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通过卡西尼公式计算佩尔和佩尔-卢卡斯多项式的反正切数列

通过将伸缩法与类似卡西尼的公式相结合，我们以封闭形式评估了关于两个反正切函数的乘积的四类和，其参数涉及佩尔多项式和佩尔-卢卡斯多项式。由此推导出斐波那契数和卢卡斯数的几个无穷级数等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Utilitas Mathematica 数学-统计学与概率论

CiteScore

0.50

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Utilitas Mathematica publishes papers in all areas of statistical designs and combinatorial mathematics, including graph theory, design theory, extremal combinatorics, enumeration, algebraic combinatorics, combinatorial optimization, Ramsey theory, automorphism groups, coding theory, finite geometries, chemical graph theory, etc., as well as the closely related area of number-theoretic polynomials for enumeration.